[[1]}]
Under Assumptions  and ,
let \(\lbrace x^k\rbrace _{k\ge 0}\)  be a sequence of random vectors produced by the
Algorithm with a proper sampling \(\hat{S}\) , and let \(x^*\)  be the optimum
of \(f\) . Then,
\(\big [f(x^{k+1})-f(x^*)\big ]\le \big (1-\sigma (\hat{S})\big )\big [f(x^k)-f(x^*)\big ] ,\) 
